Zinc Dialkyl Dithiophosphate Antiwear Tribofilm and Its Effect on the Topography Evolution of Surfaces: a Numerical and Experimental Study

Home , Zinc dithiophosphate

This is a repository copy of Zinc dialkyl dithiophosphate antiwear tribofilm and its effect on the topography evolution of surfaces: A numerical and experimental study.

White Rose Research Online URL for this paper: http://eprints.whiterose.ac.uk/100856/

Version: Accepted Version

Article: Ghanbarzadeh, A orcid.org/0000-0001-5058-4540, Piras, E, Nedelcu, I et al. (5 more authors) (2016) Zinc dialkyl dithiophosphate antiwear tribofilm and its effect on the topography evolution of surfaces: A numerical and experimental study. Wear, 362-36. pp. 186-198. ISSN 0043-1648 https://doi.org/10.1016/j.wear.2016.06.004

Reuse Unless indicated otherwise, fulltext items are protected by copyright with all rights reserved. The copyright exception in section 29 of the Copyright, Designs and Patents Act 1988 allows the making of a single copy solely for the purpose of non-commercial research or private study within the limits of fair dealing. The publisher or other rights-holder may allow further reproduction and re-use of this version - refer to the White Rose Research Online record for this item. Where records identify the publisher as the copyright holder, users can verify any specific terms of use on the publisher’s website.

Takedown If you consider content in White Rose Research Online to be in breach of UK law, please notify us by emailing [email protected] including the URL of the record and the reason for the withdrawal request.

[email protected] https://eprints.whiterose.ac.uk/ 1 Zinc Dialkyl Dithiophosphate Antiwear Tribofilm and its Effect on the Topography 2 Evolution of Surfaces: A Numerical and Experimental Study

3 Ali Ghanbarzadeh1, Elio Piras1,2, Ileana Nedelcu2, Victor Brizmer2, Mark C. T. Wilson1, 4 Ardian Morina1, Duncan Dowson1, Anne Neville1

5 1 Institute of Functional Surfaces, School of Mechanical Engineering, University of Leeds, 6 Leeds, UK 7 2 SKF Engineering and Research Centre, the Netherlands

8 Corresponding authors: 9 E-mail address: *[email protected] (Ali Ghanbarzadeh) 10 *[email protected] (Elio Piras) 11 Abstract 12 A modelling framework has recently been developed which considers tribochemistry in 13 deterministic contact mechanics simulations in boundary lubrication. One of the capabilities of 14 the model is predicting the evolution of surface roughness with respect to the effect of 15 tribochemistry. The surface roughness affects the behaviour of tribologically loaded contacts 16 and is therefore of great importance for designers of machine elements in order to predict 17 various surface damage modes (e.g. micropitting or scuffing) and to dessign more efficient 18 tribosystems. The contact model considers plastic deformation of the surfaces and employs a 19 modified localized version of Archard’s wear equation at the asperity scale that accounts for 20 the thickness of the tribofilm. The evolution of surface topography was calculated based on the 21 model for a rolling/sliding contact and the predictions were validated against experimental 22 results. The experiments were carried out using a Micropitting Rig (MPR) and the topography 23 measurements were conducted using White Light Interferometry. Numerically, it is shown that 24 growth of the ZDDP tribofilm on the contacting asperities affects the topography evolution of 25 the surfaces. Scanning Electron Microscopy (SEM) and X-ray Photoelectron Spectroscopy 26 (XPS) have been employed to confirm experimentally the presence of the tribofilm and its 27 chemistry. The effects of the contact load and surface hardnesses on the evolution of surface 28 topography have also been examined in the present work.

29 Key words: Surface Roughness, Boundary Lubrication, Tribochemistry, Wear, ZDDP

30 1. Introduction 31 Running-in is an important term used in the field of tribology. Due to the complexity and 32 diversity of the phenomena occurring in this period various definitions of the term can be found 33 in the literature (1). As described by Blau (2), running-in is a combination of processes that 34 occur prior to the steady-state when two surfaces are brought together under load and with 35 relative motion, and this period is characterized by changes in friction, wear and physical and 36 chemical properties of surfaces. During the running-in period, surface micro topography is 37 subjected to various changes. In boundary and mixed lubrication conditions, the height of the 38 asperities of rough surfaces normally decrease (3-6). However, in the case of very smooth 39 surfaces, an increase in the roughness value is observed (7, 8). During the process of change in 40 the roughness of the surfaces, load carrying capacity is increased due to the gradual 41 development of asperity-level conformity. The increase in the conformity of the surfaces is 42 significant as peaks and valleys of the surfaces correspond to each other, and the overall 43 performance of the system is improved (9-11).

44 Predicting changes in the topography of contacting bodies is important for designers to be able 45 to predict the mechanical and chemical behaviour of surfaces in loaded tribological systems. 46 The roughness of operating surfaces influences the efficiency of mechanical parts. In the 47 design of machine elements and selection of materials, the film thickness parameter, known as 48 the ratio, which is a representation of the severity of the contact, is important (12). Its value 49 is inversely proportional to the composite roughness of the two surfaces in contact. It is also 50 widely reported that fatigue life of bearing components is dependent on their functional 51 surfaces’ characteristics, such as roughness. Optimization of the surface roughness can help in 52 increasing the lifetime of bearings based on their applications (13, 14). Surface roughness can 53 enhance stress concentrations that can lead to surface-initiated rolling contact fatigue (15). 54 Therefore, it is important to be able to predict the surface topography changes in a 55 tribologically-loaded system.

56 The changes in topography can be either due to plastic deformation of the surface asperities or 57 due to removal, loss or damage to the material, which is known as wear. Evaluating wear in 58 boundary lubrication has been the subject of many studies. There are almost 300 equations for 59 wear/friction in the literature which are for different conditions and material pairs but none of 60 them can fully represent the physics of the problem and offer a universal prediction (16, 17). 61 Some examples of these models are the Suh delamination theory of wear (18), the Rabinowicz 62 model for abrasive wear (19) and the Archard wear equation (20, 21). Wear occurs by different

63 interfacial mechanisms and all these mechanisms can contribute to changes in the topography. 64 It has been widely reported that third body abrasive particles play an important role in changes 65 in the topography of surfaces. There are several parameters that govern the wear behaviour in 66 this situation such as wear debris particle size or shape, configuration of the contact and contact 67 severity etc. (22-24). It was reported by Godet (25) that a comprehensive mechanical view of 68 wear should consider the third body abrasive particles and their effect on wear and topography 69 changes. A study of abrasive wear under three-body conditions was carried out by Rabinowicz 70 et al (26). They proposed a simple mathematical model for third body abrasive wear rate and 71 showed that the wear rate in this situation is about ten times less than two-body abrasive wear. 72 It was reported by Williams et al. (27) that lubricant is used to drag the wear debris inside the 73 interface and the abrasive wear action then depends on the particle size, its shape and the 74 hardness of the materials. They reported that a critical ratio of particle size and film thickness 75 can define the mode of surface damage. Despite the importance of a three-body abrasive wear 76 mechanism there is no comprehensive mechanistic model to describe such a complicated 77 mechanism. In the mild wear regime in lubricated contacts the effect of third body abrasive is 78 often assumed to be insignificant.

79 Most of the work in the literature is based on using the well-known Archard wear equation to 80 evaluate wear in both dry and lubricated contacts. Olofsson (28-30) used Archard’s wear 81 equation to evaluate wear in bearing applications and observed the same behaviour between 82 model and experiments. Flodin (31) showed that Archard’s wear equation is good enough to 83 predict wear in spur helical gears application. Andersson et al (32) tested and reviewed different 84 wear models and reported that Archard’s wear model can predict wear of lubricated and 85 unlubricated contacts and is able to predict the surface topography both in macro and micro- 86 scales. They tested their generalized Archard’s wear model for random rough surface contact 87 (33). The Archard wear equation was widely used in numerical studies in order to predict the 88 wear and topography at different scales (34-47).

89 Hegadekatte et al. (39) developed a multi-time-scale model for wear prediction. They used 90 commercial codes to determine the contact pressure and deformations and then used Archard’s 91 wear equation to calculate wear. Andersson et al. (47) have employed the Archard wear 92 equation to predict wear in a reciprocating ball-on-disc experiment. They used a wear model 93 and implemented Fast Fourier Transforms (FFT) based contact mechanics simulations to 94 calculate contact pressure and deformations. However, in all these implementations of 95 Archard’s wear equation in numerical models, which resulted in reasonably good agreement

96 with experimental results, the effect of lubrication and lubricant properties was neglected. 97 Recently, there have been some attempts to consider the lubrication effects in boundary 98 lubrication modelling that could affect modifications to Archard’s wear equation.

99 Bosman & Schipper (48) proposed a numerical model for mild wear prediction in boundary 100 lubricated systems. They assumed that the main mechanisms that protect the boundary 101 lubricated system are the chemically-reacted layers and when these layers are worn off, the 102 system will restore the balance and the substrate will react with the oil to re-establish the 103 tribofilm. They also proposed a transition from mild wear to more severe wear by making a 104 complete wear map. In another recent work by Andersson et al. (49), contact mechanics of 105 rough surfaces was used to develop a chemo-mechanical model for boundary lubrication. They 106 used an Arrhenius-type thermodynamic equation to develop a mathematical model for 107 formation of the tribofilm on the contacting asperities. They have also employed the 108 mechanical properties of the antiwear tribofilm and used Archard’s wear equation to predict 109 wear of the surfaces. The coefficient of wear was assumed to be the same for the areas where 110 the tribofilm is formed with the areas without the tribofilm.

111 Recent work by Morales Espejel et al. (50) used a mixed lubrication model to predict the 112 surface roughness evolution of contacting bodies by using a local form of Archard’s wear 113 equation, and the model results show good agreement with experimental data. They used a 114 spatially and time-dependent coefficient of wear that accounts for lubricated and unlubricated 115 parts of the contact. The same modelling framework was used in other works of those authors 116 to predict wear and micropitting (51).

117 A range of experimental work has investigated changes in surface roughness during 118 tribological contacts. Karpinska (7) studied the evolution of surface roughness over time for 119 both base oil and base oil with ZDDP. She also studied the wear of surfaces at different instants 120 during running-in. It was suggested that a ZDDP tribofilm significantly affects the 121 topographical changes of surfaces during running-in. Blau et al. (1) stated that friction and wear 122 in running-in are time-dependent and related to the nature of energy dissipation in the contacts; 123 they are governed by a combination of different mechanical and chemical processes. They 124 showed that roughness evolution of contacting surfaces might have different patterns for both 125 surfaces, depending on several parameters.

126

127 Despite the importance and the attempts in the literature to monitor and predict the roughness 128 evolution of surfaces, there is no reported work that addresses the effect of tribochemistry. 129 However, a modelling framework has recently been developed by the authors (52),(53) that is 130 capable of predicting changes in surface topography under boundary lubrication conditions, 131 taking into account the simultaneous dynamics of an anti-wear tribofilm. The present paper 132 therefore seeks to test and exploit this model to explore the effect of a ZDDP tribofilm on the 133 evolution of surface topography. The topography evolution of both contacting surfaces is 134 predicted, taking into account not only the effects of plastic deformation and mild wear but 135 also the coupled development and influence of a ZDDP antiwear tribofilm.

136 Experimental results from a Micropitting Rig (identical to the one used in Ref (50)) are used 137 to validate the model in terms of general prediction of topography changes and growth of the 138 ZDDP tribofilm on the contacting asperities. The numerical model is described briefly in 139 Section 2, while the experimental set-up that the numerical model is adapted to is explained in 140 Section 3. The numerical results based on the model are then reported and discussed in Section 141 4, where special attention is given to the different parameters in the model that affect the surface 142 topography evolution. The importance of the growth of ZDDP tribofilm in changing the 143 topography of surfaces in the model is shown in that section. The experimental results from the 144 MPR and surface roughness measurements are reported in Section 5, where the thickness of 145 the tribofilm and the evolution of surface roughness are compared with the numerical results 146 of Section 4. Using the validated model, the effects of two important physical parameters – the 147 hardness and the load – are studied numerically in Sections 6 and 7.

148 2. Numerical model 149 The numerical model used in this work is the one reported by the authors in Ref (52). The 150 model is adaptable to tribosystems with different configurations which makes it possible to 151 investigate different problems. The model consists of three important parts:

152 (i) A contact mechanics code for rough surfaces assuming an elastic-perfectly plastic 153 material response; 154 (ii) A semi-analytical tribofilm growth model which includes both tribofilm formation 155 and partial removal; and 156 (iii) A modified Archard’s wear equation which accounts for the local thickness of the 157 ZDDP tribofilm.

158 A brief description of the model is given below; further details on parts (i) and (ii) can be found 159 in Ref (52) and an expanded discussion on part (iii) and the wear model validation is reported 160 in (53). The whole numerical model algorithm is shown schematically in Figure 1.

Initial roughness patterns, Contact inputs, End of simulation Material properties

Yes

Apply contact mechanics and No Is time = End? calculate contact pressures

(time increment)

Calculate elastic and plastic Calculate the local wear and deformations modify the surfaces

Apply plastic deformation Modify the Archard wear on surfaces equation with respect to (permanent surface the tribofilm (equation 3) modifications)

Contact temperature calculation, Modify the surfaces with Calculate local tribofilm tribofilm on top growth on surfaces

161 Figure 1. Flow chart for the numerical procedure.

162 Digitized surfaces are important inputs for the deterministic contact mechanics simulations. 163 Surfaces are generated in this work based on the model developed by Tonder (54) which is 164 based on the digital filtering of a Gaussian input sequence of numbers. This method generates 165 surfaces with desired roughness and asperity lateral size. Using artificial surface topographies 166 instead of actual surface scans does have some drawbacks, but also several advantages. For

167 practical reasons, it is good to use the measured surface topography to study different cases for 168 bearings, gears and other machine element parts. In addition, some important real 169 characteristics of the engineering surface might be missed if using artificial generated surfaces. 170 However, artificial surfaces can be used for scientific studies in different lubrication regimes, 171 and they are particularly good for performing parametric studies independently of specific 172 experimental datasets. It is possible to see the effect of different topographic properties on the 173 tribofilm formation, plastic deformation, wear and topography evolution. The method is simple 174 to manipulate and, since this work seeks to evaluate the performance of the model as a general 175 tool for exploring topography evolution, is appropriate.

176 The contact mechanics model is based on the complementary potential energy concept using 177 the model of Tian et al. (55). An elastic-perfectly plastic approach is then employed with the 178 hardness of the material to be the criterion for the plastic flow. This assumption neglects the 179 work hardening behaviour of the asperities as they deform. This method gives realistic contact 180 pressure estimation but the deformations due to the pressure can be different from real values 181 as the influence coefficients of an elastic material are used, neglecting the non-linear behaviour 182 of the yielding subsurface material. Despite its shortcomings, this method has been widely used 183 in the literature for modelling pressures and surface deformations in the elastic-plastic contacts. 184 The model is based on the contact model by Sahlin et al (56). The surfaces move relative to 185 each other and the slide-to-roll ratio determines the speed of the movement of surfaces. 186 Therefore an asperity of one surface can contact with a number of asperities on its way. The 187 movement of surfaces is periodic and is carried out by shifting the elements of matrices 188 containing the values for the asperity heights.

189 The thermal model used to calculate the flash temperature is based on the Blok theory (57). It 190 is obtained from calculation of the frictional heating. It should be noted that only the maximum 191 temperature is important in this work and using Blok’s theory seems reasonable. The 192 formulation used in this work is based on the equations reported in Kennedy and Tian (58, 59).

193 A tribochemical model was developed in the previous work of the authors that can capture the 194 growth of the tribofilm on the asperity level. The tribofilm growth is taken to be a combination 195 of the formation and partial removal at the same time (52). The formation of the tribofilm is 196 assumed to be due to tribochemical reactions and follows the reaction kinetics based on the 197 non-equilibrium thermodynamics of interfaces. The formation model is combined with a

198 phenomenological term that accounts for the simultaneous partial removal of the tribofilm, 199 giving the net development of the tribofilm thickness as a function of time:

200 201 where and are the Boltzmann and the Planck constants respectively, is the flash 202 temperature and and are constants accounting for the continuous partial removal of the 203 tribofilm. Hence the tribofilm is modelled as a dynamic system such that even when an 204 equilibrium thickness is achieved, formation and partial removal continue but balance each 205 other to maintain that thickness. Note that t in equation (1) refers to a local time for each point 206 in the domain, and starts increasing at a given point once an asperity contact occurs there. The 207 term captures the effect of rubbing in inducing the tribochemical reactions. As reported 208 recently (60), mechanical activation plays an important role in the growth behaviour of the 209 tribofilm on a single asperity. Gosvami et al. (60) showed that the rate of tribochemical reaction 210 is highly dependent on the pressure applied on a single asperity. This is in line with the model 211 presented above, where the role of mechanical activation is represented by the term . A 212 detailed discussion can be found in the previous work (52).

213 At this point it is important to distinguish between the wear of the tribofilm, which is captured 214 by the ‘partial removal’ term in Equation (1), and the wear of the substrate itself. Henceforth 215 in this paper the term ‘wear’ will be used to refer to the (mild) wear of the substrate underneath 216 the tribofilm – i.e. the wear of the substrate in the presence (and, initially, absence) of the 217 tribofilm. Studies of ZDDP tribofilms on steel show that the tribofilm contains substrate atoms 218 at a concentration that decreases towards the top of the tribofilm. Hence material from the 219 substrate is consumed in forming (and maintaining) the tribofilm, and therefore if part of the 220 tribofilm is removed due to the contact, this corresponds to an effective removal of material 221 from the substrate. This principle is the basis of the mild wear model of Bosman & Schipper 222 (Ref (48)), who linked the rate of substrate wear to the rate of tribofilm removal by considering 223 the volumetric percentage of iron as a function of depth in the tribofilm. The functional form 224 was determined from X-ray photoelectron spectroscopy analysis.

225 In the present work, the link between the substrate wear and the tribofilm takes a different form. 226 The details are explained elsewhere (53) but, in brief, the wear model is a modified version of 227 Archard’s wear equation in which the wear coefficient is related to the local tribofilm thickness. 228 The local wear depth of each point at the surface is given by:

229 (2) 230 in which , , , , and are the material hardness, dimensionless Archard’s wear 231 coefficient, local contact pressure, sliding speed, and time step respectively. All the parameters 232 in Equation (2) except are calculated in the contact mechanics simulation. The decrease 233 in the concentration of substrate atoms within the tribofilm as the distance from the 234 substrate/tribofilm interface increases supports the fact that less wear of the substrate occurs if 235 a thicker tribofilm exists. Hence it is assumed that the coefficient of wear is at its maximum for 236 steel-steel contact (i.e. when no tribofilm is present) and at its minimum when the tribofilm has 237 its maximum thickness. Assuming, in addition, a linear variation with tribofilm thickness h, 238 the coefficient of wear is given by:

239 (3) 240 where is the coefficient of wear for a substrate covered by a tribofilm with thickness .

241 and are the coefficients of wear for steel and for the maximum ZDDP tribofilm 242 thickness respectively, and is the maximum tribofilm thickness. The values of and 243 are determined from a single calibration experiment as described in Section 4. Figure 1 244 shows a flow chart of the numerical model.

245 3. Experimental setup 246 The tests were carried out using a Micropitting rig (MPR) which is shown schematically in 247 Figure 2.

248

249 Figure 2. The load unit of the Micropitting Rig (MPR)

250 The principle part of the Micropitting rig is the load unit which includes a spherical roller 251 12mm in diameter (taken from a spherical roller bearing), which comes into contact with three

252 larger counterbodies (which are in fact inner rings of a cylindrical roller bearing). The roller 253 and the rings can be ground and/or honed and finished to any desired roughness on the surface. 254 With this configuration, the roller accumulates loading cycles 13.5 times faster than any of the 255 three rings during a test. The oil is carried into the contact by the two bottom rings, creating 256 the conditions of fully lubricated contact – depending, of course, on the desired lubrication 257 regime.

258 The maximum load that can be applied on the machine is 1250 N, corresponding to a maximum 259 Hertzian pressure of 2.75 GPa, which is high enough for bearing studies. The temperature can 260 be controlled up to 135ºC and the maximum tangential speed is 4 m/s.

261 The roller and rings are driven by two independent motors, which means that a controlled slide- 262 to-roll ratio of ±200% can be reached. The size of the Hertzian contact varies with the load and 263 the transverse radius of the roller, but the typical values are around 0.244  1.016 mm (in the 264 rolling and transverse direction, respectively) corresponding to the maximum Hertzian contact 265 pressure of 1.5 GPa. The operating conditions used in the present work are listed in Table 1. 266 The oil temperature, load, speed and slide-to roll ratio were maintained constant during the 267 experiments. The roughness was changed (on the rings only), to simulate different lubrication 268 conditions.

269 Over a given experiment duration, the number of rolling cycles experienced is different for the 270 roller and the rings; in fact each cycle of the rings corresponds to 13.5 cycles of the roller.

271 The lubricant used was a synthetic model oil (poly-alpha-olephine, PAO) mixed with 1% 272 weight of primary zinc dialkyl dithiophosphate (ZDDP). The properties of the oil and additive 273 are listed in Table 2.

274

275

276

277

278

279

280 Table 1. List of experimental test conditions for the Micropitting rig Temperature 90ºC

Entrainment speed ( ) 1 m/s

Slide-to-roll ratio ( ) 2% Hertzian contact pressure 1.5 GPa

Lubricants PAO + ZDDP 1%

Number of cycles for roller 20, 50, 100 kcycles

Number of cycles for rings 1.48, 3.7, 7.4 kcycles

R.M.S. roughness roller 50±10 nm

R.M.S. roughness rings 100±20nm, 200±20nm, 600±50 nm

Value of ratio 0.58, 0.3, 0.1

281

282 Table 2 Properties of base oil and additive used for experiments. Kinematic Kinematic Sulphur Phosphorus Code viscosity 40°C viscosity 100°C content content (mm2/s) (mm2/s) (wt%) (wt%) Synthetic Oil 56.2 9.84 0.01 0.00

Primary ------23.4 11.3 ZDDP (C8) 283

284 For each roughness value, tests with different running times were carried out in order to obtain 285 the evolution of roughness during the running-in period. In each new test, the roller was 286 replaced with a fresh roller having the same initial roughness ( = 50±10nm). The same ring

287 samples were used in each set of experiments (i.e. for a particular roughness), but each time 288 the contact with the roller was at a different, previously unused, position along the width of the 289 rings. The advantage of testing the same ring at different positions along its width is that the 290 variability of the ring surface topography is kept to a minimum. Hence each test within a set of

291 experiments began with a fresh roller/ring surface contact having, as closely as possible, the 292 same initial conditions. Monitoring of the friction coefficient throughout the tests of different 293 duration showed excellent agreement between tests at corresponding times. The whole process 294 was repeated with a fresh set of rollers and rings to assess the reproducibility of the results. The 295 same changes in roughness were observed over time, indicating that the evolution of the surface 296 topography is reproducible, however there were – as expected – differences in the actual r.m.s. 297 values of roughness at corresponding times, which are reflected in the error bars of the figures 298 presented later.

299 After each test, the samples were cleaned in an ultrasonic bath with petroleum ether for 5 300 minutes and then the roughness was measured using White Light Interferometry (Wyko 301 NT1100). As shown in other work (50), the presence of a tribofilm can interfere with the 302 measurements of roughness using White Light Interferometry. The roughness of interest is the 303 roughness of the steel surface and to be able to measure it, the tribofilm had to be removed. 304 The technique consisted of covering the wear track with a drop of ethylenediaminetetraacetic 305 acid (EDTA); the EDTA dissolves the tribofilm and then it is removed with a tissue after 20 306 seconds by just rubbing the wear track. The roughness of each roller sample was accurately 307 measured at 5 different circumferential locations along the contact track. The same process for 308 roughness measurements was repeated for each of the rings and then the roughness r.m.s.value

309 was obtained by averaging all the measured Rq values. Changes in Rq values for the roller and 310 the three rings were monitored with time. Figure 3 shows example roughness profiles.

311 The morphology of ZDDP-derived reaction layers was observed with a Zeiss Supra 55 312 scanning electron microscope (SEM) using 5 kV electron beam voltage in the secondary 313 electron mode. Analysis of the chemical composition of the ZDDP-derived tribofilm was made 314 by means of X-ray photoelectron spectroscopy (XPS) using a PHI 5000 Versa Probe 315 Spectrometer (Ulva-PHI Inc, Chanchassen, MN, USA) equipped with a monochromatic Al k 316 source (1486.6 eV). The data were collected with a beam size of 100 µm and a power of 25W 317 in the FAT analyzer mode. The pass energy was 117.0 eV with energy step size of 1 eV for 318 Survey scan and 46.95 eV with an energy step of 0.1 eV for high resolution spectra. During all 319 the measurements the pressure was always below 10-7 Pa.

320 The identification of the wear track was performed by Scanning X-ray images (SXI) collected 321 in an area of 11 mm2, allowing the identification of the different analysis locations inside the 322 wear track.

Roller

Initial Surface After 100 kcycles

Rings

Initial Surface After 7.4 kcycles (of the rings)

323 Figure 3. Example of Wyko roughness measurements (all values are in micro metre).

324 XPS data were processed by using CASA XPS software (version 2.3.16, Casa Software Ltd, 325 UK). The detailed spectra were fitted with Gaussian/Lorentzian curves after linear background 326 subtraction. Charge effect is taken into account by referring to C 1s Binding Energy at 285.0 327 eV.

328 The profile of the chemical composition of the ZDDP-derived tribofilm were obtained by using 329 an Ar+ ion gun source with an energy of 2 keV, 22 mm2 area, 10 µA sputter current and 60s 330 of waiting time before spectra acquisition. The sputtering rate for the tribofilm was found to be 331 4.5 nm/min using optical profilometry and measuring the wear depth after 10 min of sputtering. 332 Sputtering depth profiles were processed by using MultiPack™ Software (version 8.3, 333 ULVAC-PHI Chanchassen, MN, USA), and the reaction layer thickness was defined as the 334 thickness where the atomic concentration of O1s signal is less than 5% for steel samples. The 335 sputtering time provides the measures of layer thickness.

336 The surface composition and morphology was analyzed by X-ray photoelectron spectroscopy 337 (XPS) and scanning electron microscopy (SEM) coupled with energy-dispersive X-ray 338 spectroscopy (EDX) before roughness measurements.

339 The specimens used were made of steel AISI 52100 (chemical composition shown in Table 3), 340 with elastic modulus of 210 GPa and a Poisson’s ratio of 0.27.

341 Table 3 Chemical properties of steel AISI 52100 in %

Cr Ni Mn Mo Si C S Cu AISI 52100 1.350 0.250 0.450 0.100 0.350 1.050 0.015 0.030 342

343 4. Numerical results and discussion 344 The Micropitting rig (MPR) experiments, the results of which will be discussed in the next 345 section, were simulated with the numerical model. The contact mechanics model was adapted 346 to the same configuration as the MPR. It should be noted that the roughness of the surfaces is 347 characterized by a reasonably large area of the surfaces. Using such large areas as input into 348 numerical model makes it computationally expensive to simulate, especially for the high 349 numbers of loading cycles that result in the evolution of surface topography. In principle, the 350 study area should cover at least several wavelengths of the surface in order to be reasonable. 351 For the surfaces used in this work, an average wavelength of 15 to 20 µm was identified.

352 Simulations were conducted with different domain sizes to establish the most appropriate size 353 to ensure numerical accuracy while minimizing the computational effort and hence simulation 354 time required. It was found that a computation domain of 64µm×64µm area consisting of 64 355 nodes of one micron size in each dimension was the minimum domain needed; domain sizes 356 below this were found to be unreliable. This size covers 3-4 roughness ridges, and it is known

357 that at least 3 roughness ridges should be resolved to be able to track the surface topography 358 evolution. To enable simulations over many cycles in a reasonable time, the 64µm×64µm 359 domain was used in all the simulations presented here.

360 Because of the high number of loading cycles it is not possible to simulate all the loading 361 cycles, even with the smallest appropriate domain size, so numerical experimentation was 362 conducted to optimize the simulation time and the frequency with which the topography was 363 updated. Selection of the size of the wear time-step is dependent on several parameters, the 364 most important of which are the contact pressure, yield stress of the solid, coefficient of wear 365 and the lubrication regime. For this reason it was decided to have finer time-steps in the 366 beginning of the contact, due to higher plastic deformations, and have bigger time steps 367 following that. Hence over the first 100 load cycles, the geometry was updated after every 368 loading cycle. Thereafter the geometry was modified after every 100 loading cycles to increase 369 the time efficiency of the simulations.

370 The numerical model follows a semi-deterministic approach so that some parameters in the 371 model should be calibrated prior to any predictions. One important calibration parameter is the 372 initial coefficient of wear used in the wear model. To determine this, simulations were run with 373 different initial coefficients of wear and the predicted wear in each case was compared with 374 that observed in one particular experimental test. The initial coefficient of wear giving the 375 closest match with the experiment was then used for the rest of the simulations.

376 The other important parameters in the model are the tribofilm growth model parameters of 377 Equation 1. These parameters ( , , and ) are obtained by fitting the mathematical 378 expression of Equation 1 to experimental tribofilm thickness results. Ideally, for best accuracy, 379 measurements of the tribofilm thickness from specific MPR experiments presented here should 380 be used for calibration. However, this was not possible because the measurement of the 381 tribofilm thickness on the rings and rollers was experimentally cumbersome, and furthermore 382 would have produced insufficient data points to allow fitting of Equation 1. Therefore, in this 383 paper, the calibration parameters are actually the ones reported previously in Ref (52), which 384 were obtained using experimental tribofilm thickness measurement results reported in Naveira 385 Suarez et al. (61). Although that work used a different experimental arrangement, the materials 386 used (Steel AISI 52100 and PAO oil with ZDDP antiwear additive) were the same as those in 387 the present work. Hence the same calibration parameters (presented in Table 4) were used in 388 this work for simplicity.

389 Inevitably a semi-deterministic model such as the one used here involves a number of 390 parameters that must be determined by reference to experimental data. It is therefore natural to 391 ask: what is the sensitivity of the model to the values of these parameters, and how can such 392 parameters be determined in the absence of experimental data? Importantly, in the results 393 presented here, two key elements of the model, namely the initial specific topography of the 394 surfaces and the tribofilm formation parameters, were effectively obtained independently of 395 the MPR experiments. For the tribofilm parameters ( , , and ), values from a 396 different study using the same materials but different configuration were used. For the surface 397 topography, artificial surfaces were created with roughness and lateral asperity size matching 398 the experiments. Indeed, the model of equation (1) has been adapted to the pool of experimental 399 results available in the literature, to provide a good indication of the range of the parameters 400 and to allow selection of a reasonable set of calibration parameters in the absence of specific 401 experimental data (see Ref (62)).

402 Table 4 The calibration parameters

Parameter Value Description

× Dimensional wear coefficient for steel ( ) × Dimensional wear coefficient for maximum film thickness ( ) 176 Maximum local tribofilm thickness in the formation process (nm)

4.13× Tribofilm formation rate constant 0.1125 Tribofilm removal constant

0.0006799 Tribofilm removal exponential factor

209 Young’s modulus of two surfaces ( GPa)

0.3 Poisson’s ratio

8 Hardness of the steel substrate ( GPa)

2 Hardness of the tribofilm at steady state tribofilm thickness ( GPa)

403

404 The growth of the tribofilm is assumed to occur only at contacting asperities. Therefore the 405 local contact properties calculated from the contact model are responsible for the formation of 406 the tribofilm at the asperity scale. It is observed experimentally that the formation of the 407 tribofilm on asperities can lead to change in the mechanical properties of interfaces and also

408 results in an increase in load-carrying capacities of the contacting bodies (63). The tribofilm 409 has been reported as a solid-like material with different mechanical properties from the 410 substrate (64-66). The difference in the mechanical properties of ZDDP tribofilm at different 411 areas in the bulk was related to the different chain lengths of polyphosphate, with shorter 412 polyphosphates being present deeper in the tribofilm and longer chains existing close to the 413 surface of the film (67-70). In the current model, the values of the tribofilm hardness at the 414 surface and near the substrate can be approximated from experimental results (71). This 415 variation is assumed to be between 2 and 6 GPa, changing linearly from the surface to the 416 substrate. This is a gross assumption but, given the lack of experimental data on the specific 417 form of this variation, it seems reasonable. In addition, the elastic properties of the tribofilm 418 also vary from the surface to the bulk and this variation is related to hardness variations (72).

419 Once the tribofilm, which is a solid–like material, forms on the contact asperities, the 420 topography of the surfaces is changed and the contact conditions between surfaces may change 421 as a result. This change in the contact conditions can lead to a different topographical evolution 422 at the interface in comparison to the case when no such tribofilm is formed. This effect can be 423 seen in the numerical results.

424 One example of the model results is shown in Figure 4. It can be seen that the rougher surface 425 (Figure 4 (a) left) starts to become smoother in the beginning of the contact then gradually 426 becomes rougher over time. It can be interpreted that in the beginning of the contact the 427 dominant plastic deformation can lead to relatively fast surface deformations. The tribofilm 428 formed on the surfaces will change the local mechanical properties of the surfaces as well as 429 their micro-geometry. An increase in the roughness of the rougher surface can occur because 430 of the growth of the tribofilm, which is a solid-like material. Fast growth of the tribofilm on 431 the highest asperities in the running-in stage changes the geometry of those asperities in the 432 contact. The new asperity consists of a substrate (steel) and the glassy polyphosphate tribofilm 433 on top, which is a solid-like material. It can come into contact with the counterbody and 434 increase the average peak-to-valley height difference. The counter body also consists of a 435 tribofilm on top but, in the running-in stage, there are numerous asperities that are not covered 436 by the tribofilm yet. This will lead to the contact of the high asperities consisting of tribofilm 437 into the asperities of the counterbody that are not yet covered by the tribofilm. After some time, 438 the surface becomes gradually smoother because of the mild wear occurring at the contacting 439 asperities. Different stages of the simulation are numbered in Figure 4. Point 0 is the beginning

440 of the simulation where the initial surfaces are not in contact yet. Point 1 is the time after 20 441 kcycles of the roller. It is the time by which the highest asperities of the surfaces are plastically 442 deformed. Point 2 is selected to be the end of the experiments (after 100 kcycles of the roller). 443 These points are selected and indicated in Figure 4 as reference times that are used in Figure 5 444 and Figure 6 to study the difference in the surface topography and tribofilm formation, 445 respectively, at different times of the simulation. Note that the number of cycles for the ring 446 and the roller are different at Points 1 and 2, and therefore the horizontal axis scales are different 447 in Figure 4-a and Figure 4-b, but these points correspond to the same physical time.

Point 0 Point 1 Point 2

448

Figure 4 (Left) Roughness evolutions and (Right) tribofilm build up for the (a) rougher (ring) and (b) smoother (roller) body as predicted by the model, for the case of initial ring roughness 600 nm.

449 In the beginning of the contact, the highest asperities of the rough surface experience high 450 levels of plastic deformation, which results in smoothing of the rough surface. Simulation 451 results to confirm this are shown in Figure 5. It can be seen in the figure that the asperities of 452 the initial surface (Figure 5-a) are smoothed (Figure 5-b) after 20 kcycles of the roller. The 453 asperities are then smoothed further due to mild wear (Figure 5-c). On the other hand, contact 454 between the smooth surface and the highest asperities of the rough surface produces 455 indentations in the smooth surface (Figure 5d-f). Growth of the tribofilm on the contacting

456 asperities then results in roughening of the rough surface. The simulation results of the 457 inhomogeneous tribofilm formed on the surface confirms this and the results are shown in 458 Figure 6. It can be seen that the tribofilm grows on the contacting asperities both in thickness 459 and coverage.

µm µm

460

Figure 5 Surface topography evolution predicted by the model (a) surface of the ring before the experiment point 0 (b) surface of the ring at point 1 (c) surface of the ring at point 2 (d) surface of the roller before the experiment point 0 (e) surface of the roller at point 1 (f) surface of the roller at point 2 461

462 This growth of the tribofilm is responsible for the increase in the roughness of the ring. The 463 growth of the tribofilm on both rough (ring) and smooth (roller) surfaces are shown in Figure 464 6. It can be seen that the growth on the roller (smooth surface) is faster in comparison to the 465 ring (rough surface), since the roller experiences 13.5 times more loading cycles in a given 466 time period and the growth of the tribofilm on the surfaces is directly proportional to the time 467 of rubbing.

468 The smoother body (roller) experiences a relatively fast initial decrease in the roughness value 469 (see Figure 4). The root mean square sharply decreases from 0.05 µm to about 0.047 µm; this 470 is because of high plastic deformation and decrease in the height of the highest peaks on the 471 smooth surface. Then an overall increase in the roughness of the smoother surface is observed 472 because of contact with a rougher surface and also fast growth of the tribofilm. Similar results 473 were obtained in (50). It should be noted that the tribofilm is formed on both surfaces and the 474 corresponding average tribofilm thickness is shown in Figure 4 parallel to the roughness 475 evolution of both surfaces for comparison purposes. The next section describes the results of 476 experiments carried out to validate the model and to confirm its predictions of the changes in 477 the topography of the surfaces.

478 5. Experimental results 479 The roughness evolution of the MPR roller and the three different rings obtained by the method 480 described in Section 3 is shown in Figure 7. The figure shows that when the roughness of the 481 rings is higher, longer running-in will occur which delays the tribofilm build up and the surface 482 modifications at the beginning are very similar to those found without the presence of additives. 483 With smoother surfaces, the roughness modifications decrease because of the formation of a

484 tribofilm. When the contact is in the EHL regime ( rings=100 nm), the process is mainly

485 governed by the coverage of the contacting asperities with ZDDP tribofilm. The asperities of 486 the bodies covered with a tribofilm promote the roughening of the ring’s surface until it reaches 487 the steady state. This can be noticed because the differences in roughness are not visible during 488 the initial cycles on the smoother body. It is clear that, when the contact is in the boundary or

489 mixed lubrication regimes ( rings=600 nm and rings=200 nm, respectively), the first process

490 which occurs on the surface is the plastic deformation of asperities, leading to a smoothing of 491 the surface and this is in agreement with the numerical results reported in Section 4. In complete

492 boundary lubricated contact ( rings=600 nm), after the plastic deformation process, the

493 tribofilm can increase the roughness of the surfaces.

494

495 Figure 6 Tribofilm growth on the contacting asperities (a) at point 1 for rough surface (ring) (b) at point 2 for rough surface (ring) (c) at point 1 for smooth surface (d) at 496 point 2 for smooth surface

497

498 Figure 7 Experimental results on different roughness of rings

499 The numerical model is only valid for boundary lubrication conditions. Therefore, for 500 validation purposes, it was necessary to compare numerical results with the experiments in 501 boundary lubrication regime. Although this is one of the shortcomings of the numerical 502 framework, it is important to develop robust models in boundary lubrication that are able to 503 capture tribochemistry phenomena. The experimental topography measurements for the case

504 of boundary lubrication ( rings=600 nm), are shown in Figure 8 for comparison purposes.

505 Good qualitative agreement is seen between the experimental (Figure 8) and the model (Figure 506 4) results. It is demonstrated in the model that the roughness of both smooth and rough 507 contacting surfaces will converge to specific values but they will never reach the same number 508 (see also (50)). It was also shown that different surface roughness configurations would have 509 different topography behaviour. The initial roughnesses of both contacting surfaces are the key 510 parameters which govern the further roughness evolution. It was assumed in the numerical 511 results of Section 4 that the tribofilm growth on the contacting asperities is responsible for the 512 roughening of the rings. The numerical results for tribofilm growth were then presented in the 513 same section. To confirm this by means of experimental data, surface analysis results of the 514 tribofilm formed on the surface are reported here.

Number of Cycles Rings (x1000 ) 0 2 4 6 8 700

600

500

400 Roller Ring

300 RoughnessRq(nm) 200

100

0 0 20 40 60 80 100 120 Number of Cycles Roller (x1000) 515

516 Figure 8 Roughness measurement experimental results for both ring and roller

517 Figure 9 shows an SEM image of the tribofilm in the middle of the wear track formed on the 518 roller. It can be seen from the image how the tribofilm is formed on the wear track due to severe 519 conditions. It can be compared to the numerical results of Figure 6 and a similar pattern can be 520 observed. The image is taken at the end of the experiment in the boundary lubrication regime

521 when the initial roughness of the ring was rings=600 nm.

522 XPS analysis performed on the tribofilm showed the oxygen signal with two different peaks. 523 According to the literature, these peaks belong to two different oxygen types: the main peak at 524 531.6 eV is assigned to the non-bridging oxygen (NBO) in poly(thio)-phosphate chains and 525 also to other oxygen-containing groups such as sulphates, carbonates or hydroxides (73); the 526 second peak at 532.8 eV can be assigned to the presence of the bridging oxygen (BO) which 527 corresponds to P-O-P and P-O-C bonds (73). The P 2p signal was detected at 133.4 eV while 528 the Zn 3s at 140.0 eV. S 2p signal was found on the surface at 161.8 eV which is attributed to 529 the oxidation state of -2 as found in sulphides (74) and thiolates (75) or when sulphur is 530 substituting oxygen atoms in a phosphate (73).

531 Figure 10 shows the XPS depth profile of the tribofilm formed on the surface of the ring in the 532 boundary lubrication regime. The thickness of the tribofilm was found to be about 55 nm, 533 which is consistent with the prediction of the numerical model (see Figure 4 (a), right). 534 According to previous studies (68), the tribofilm is composed of phosphate chains, the length 535 of which can be determined by the ratio between bridging oxygen and non-bridging oxygen 536 (76). As Figure 11 shows, in this case, the ratio is approximately 0.25, which corresponds to 537 the presence of polyphosphate chains, i.e. chains of more than 3 phosphate groups (76, 77). A 538 similar value of the ratio was also obtained for the mixed lubrication regime. The 539 polyphosphate chain length influences the local mechanical properties of the tribofilm on the 540 surface, and different mechanical behaviour such as the durability of the films (63-65, 78). For 541 this reason, the chemical characteristics of the film are important parameters in defining the 542 physical and mechanical behaviour of the film and the corresponding changes in the 543 topography of the surfaces. The surface analysis results shown in Figure 9 and Figure 10 544 indicate that the tribofilm covers the surface asperities of the roller. In the numerical simulation 545 results of Section 4, growth of such a tribofilm was reported to be the reason for the increase 546 of roughness of the ring surface.

547

548 Figure 9 SEM image of the tribofilm formed on the wear track

549

550 Figure 10 XPS depth profile of the tribofilm formed on the surface of the ring

0.5

0.4

0.3 Mixed Boundary

0.2 Ratio BO/NBO

0.1

0.0 551

552 Figure 11. Ratio BO/NBO for the two lubricating conditions

553

554 6. Effect of load on surface topography evolution 555 Having been validated against the experimental measurements, the numerical model can be 556 used to conduct wider parametric studies to explore the influence of important factors such as 557 contact load and material hardness on the evolution of the surface topography. To illustrate,

558 simulations were carried out for different contact loads to see the effect on the roughness 559 evolution of the rings with initial roughness 600 nm. The results are shown in Figure 12. The 560 selected contact pressures were between 700 MPa and 2 GPa in order to see the effect of a 561 relatively wide range of loads. It should be noted that even with the lowest load the ratio was 562 small enough that the contact was in the boundary lubrication regime.

563

564 Figure 12 Simulation of roughness evolution of the rings at different contact loads

565 In this specific contact configuration, it is observed that the higher loads change the surface 566 roughness more than the lower loads, which is consistent with the expected higher plastic 567 deformation. Clearly the load does influence the evolution of the surface roughness, but the 568 differences in the magnitude of plastic deformation are not significant as can be seen from the 569 results in Figure 12. For instance, doubling the contact pressure from 1 to 2 GPa results in a 570 difference in roughness of around 60 nm, or about 12%, at 7000 cycles of the rings. The same 571 pattern in results were reported by Wang et al (79) and also confirmed by Jamari (80).

572 7. Effect of surface hardness on topography evolution 573 Simulations have been also carried out for different material hardnesses and the results are 574 shown in Figure 13. The hardness of the contacting bodies influences the elastic-plastic 575 behaviour and directly affects the time changes in the surface topography. Because the contact 576 code formulation was developed for similar materials, the hardness mentioned here was the

577 hardness of both contacting surfaces. In this study, the hardness variation was from 4 GPa to 578 12 GPa. It can be seen from the results that the harder materials experienced less plastic 579 deformation and also less variation in topography due to either plasticity or wear. As mentioned 580 in the numerical model of Section 2, the material hardness is the criterion for plastic flow. 581 Higher hardness results in less plastic deformation of the surfaces and it consequently results 582 in less change in the topography. Softer materials are more likely to deform and experience 583 larger variations in topography. In addition, based on the formulation of Archard’s wear 584 equation, harder materials are less prone to wear (see equation 2).

585

586 Figure 13 Simulation of roughness evolution for materials of different hardnesses

587 8. Conclusions 588  The predictions of the emerging topography were validated against experiments carried 589 out using a Micropitting rig. The surface topography is affected by surface plastic 590 deformations, tribofilm growth and wear. It is shown that during initial contact, high 591 plastic deformations on the surfaces are responsible for rapid initial changes in the 592 topography. 593  Results also show that growth of a tribofilm can change the local mechanical properties 594 at interfaces which can influence the further roughness evolution of the surfaces. One 595 interesting conclusion from an analysis of the pool of numerical simulations is that the

596 roughness evolution of both contacting bodies is significantly influenced by the initial 597 roughness patterns. It means that the initial roughness of both surfaces in combination 598 will determine the mode of topography evolution and hence a proper finishing of both 599 contacting surfaces is required to obtain a better tribological performance in the steady- 600 state. 601  The growth of polyphosphate tribofilm formed on the contacting asperities is 602 responsible for an increase in the roughness of the surfaces in contact. This was shown 603 numerically (in Section 4) and verified with experimental measurements (Section 5) of 604 roughness (after removal of the tribofilm). Experimental surface analysis also showed 605 that a tribofilm was formed on the surface with a thickness very close to the predicted 606 values. 607  Clearly a model is more general and more useful if it is able to predict the key behaviour 608 of a system without having to rely on very specific details and measurements of 609 individual experiments. Therefore the good qualitative agreement between the 610 predicted behaviour of the system and the experimental observations is very 611 encouraging.

612

613 9. Acknowledgements 614 This study was funded by the FP7 program through the Marie Curie Initial Training Network 615 (MC-ITN) entitled “ENTICE - Engineering Tribochemistry and Interfaces with a Focus on the 616 Internal Combustion Engine” [290077] and was carried out at the University of Leeds and the 617 SKF Engineering & Research Centre in the Netherlands. The authors thank all ENTICE 618 partners for useful discussions on the topic and the methodology.

619

620

621

622

623

624

625

626

627 References

628 1. Blau PJ. On the nature of running-in. Tribology International. 2006;38(11):1007-12. 629 2. Blau PJ. Running-in: Art or engineering? Journal of materials engineering. 1991;13(1):47-53. 630 3. Atala H, Rowe G. Surface roughness changes during rolling. Wear. 1975;32(2):249-68. 631 4. Masouros G, Dimarogonas A, Lefas K. A model for wear and surface roughness transients 632 during the running-in of bearings. Wear. 1977;45(3):375-82. 633 5. Dong W, Stout K. An integrated approach to the characterization of surface wear i: Qualitative 634 characterization. Wear. 1995;181:700-16. 635 6. Jeng YR, Lin ZW, Shyu SH. Changes of surface topography during running-in process. Journal 636 of tribology. 2004;126(3):620-5. 637 7. Karpinska A. Running-in and the evolution of metallic surfaces subjected to sliding and rolling 638 contact: Imperial College London; 2010. 639 8. Chou C, Lin J. Tribological effects of roughness and running-in on oil-lubricated line contacts. 640 Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology. 641 1997;211(3):209-22. 642 9. Tyagi MR, Sethuramiah A. Asperity level conformity in partial EHL. Part I: Its characterization. 643 Wear. 1996;1(197):89-97. 644 10. Sreenath A, Raman N. Mechanism of smoothing of cylinder liner surface during running-in. 645 TRIBOLOGY international. 1976;9(2):55-62. 646 11. Sreenath A, Raman N. Running-in wear of a compression ignition engine: factors influencing 647 the conformance between cylinder liner and piston rings. Wear. 1976;38(2):271-89. 648 12. Neale MJ. The tribology handbook: Butterworth-Heinemann; 1995. 649 13. Goepfert O, Ampuero J, Pahud P, Boving H. Surface roughness evolution of ball bearing 650 components. Tribology transactions. 2000;43(2):275-80. 651 14. Tripp J, Ioannides E, editors. Effects of surface roughness on rolling bearing life. Japan 652 International Tribology Conference II; 1990. 653 15. Nélias D, Dumont M, Champiot F, Vincent A, Girodin D, Fougeres R, et al. Role of inclusions, 654 surface roughness and operating conditions on rolling contact fatigue. Journal of tribology. 655 1999;121(2):240-51. 656 16. Meng H, Ludema K. Wear models and predictive equations: their form and content. Wear. 657 1995;181:443-57. 658 17. Meng H-C. Wear modeling: evaluation and categorization of wear models. 1994. 659 18. Suh NP. An overview of the delamination theory of wear. Wear. 1977;44(1):1-16. 660 19. Rabinowicz E. Friction and wear of materials. 1965. 661 20. Archard J. Contact and rubbing of flat surfaces. Journal of applied physics. 1953;24(8):981-8. 662 21. Holm R, Holm EA. Electric contacts. 1967. 663 22. Stachowiak G, Stachowiak G. The effects of particle characteristics on three-body abrasive 664 wear. Wear. 2001;249(3):201-7. 665 23. Dwyer-Joyce R. Predicting the abrasive wear of ball bearings by lubricant debris. Wear. 666 1999;233:692-701. 667 24. Dwyer-Joyce R, Sayles R, Ioannides E. An investigation into the mechanisms of closed three- 668 body abrasive wear. Wear. 1994;175(1):133-42. 669 25. Godet M. The third-body approach: a mechanical view of wear. Wear. 1984;100(1):437-52. 670 26. Rabinowicz E, Dunn L, Russell P. A study of abrasive wear under three-body conditions. Wear. 671 1961;4(5):345-55. 672 27. Williams J, Hyncica A. Mechanisms of abrasive wear in lubricated contacts. Wear. 673 1992;152(1):57-74. 674 28. Olofsson UA, Sören Björklund, Stefan. Simulation of mild wear in boundary lubricated 675 spherical roller thrust bearings. Wear. 2000;241(2):180-5.

676 29. Olofsson U, Dizdar S. Surface analysis of boundary-lubricated spherical roller thrust bearings. 677 Wear. 1998;215(1):156-64. 678 30. Ulf Olofsson SrA, Stefan Bjorklund. Simulation of mild wear in boundary lubricated spherical 679 roller thrust bearings. Wear. 2000;241(2):180-5. 680 31. Flodin A. Wear of spur and helical gears. Royal Institute of Technology, Stockholm, Doctoral 681 Thesis. 2000. 682 32. Andersson S, Olofsson U, editors. Towards a general model for wear simulation. IRG-OECD 683 Meeting, Uppsala, Sweden; 2005. 684 33. Andersson S, Söderberg A, Olofsson U. A random wear model for the interaction between a 685 rough and a smooth surface. Wear. 2008;264(9):763-9. 686 34. E.M. Bortoleto ACR, V.Seriacopi,F.J.Profito,D.C.Zachariadis,I.F.Machado,, A. Sinatora RMS. 687 Experimental and numerical analysis of dry contact in the pin on disc test. Wear. 2012;301(1):19-26. 688 35. Priit Podra SA. Simulating sliding wear with finite element method. Tribology international. 689 1999;32(2):71-81. 690 36. Öqvist M. Numerical simulations of mild wear using updated geometry with different step size 691 approaches. wear. 2001;249(1):6-11. 692 37. V Hegadekatte NHaOK. Finite element based simulation of dry sliding wear. modelling and 693 simulation in materials science and engineering. 2005;13(1):57. 694 38. V. Hegadekatte S. Kurzenha NH, O. Kraft. A predictive modeling scheme for wear in 695 tribometers. Tribology international. 2008;41(11):1020-31. 696 39. V. Hegadekatte J. Hilgertb OKNH. Multi time scale simulations for wear prediction in micro- 697 gears. Wear. 2010;268(1):316-24. 698 40. Bosman R, Schipper DJ. Running-in of systems protected by additive-rich oils. Tribology 699 Letters. 2011;41(1):263-82. 700 41. G.K. Sfantos MHA. Wear simulation using an incremental sliding Boundary Element Method. 701 Wear. 2006;260(9):1119-28. 702 42. Sfantos G, Aliabadi M. A boundary element formulation for three-dimensional sliding wear 703 simulation. Wear. 2007;262(5):672-83. 704 43. Ilincic S, Vernes A, Vorlaufer G, Hunger H, Dörr N, Franek F. Numerical estimation of wear in 705 reciprocating tribological experiments. Proceedings of the Institution of Mechanical Engineers, Part J: 706 Journal of Engineering Tribology. 2013;227(5):510-9. 707 44. Ilincic S, Vorlaufer G, Fotiu P, Vernes A, Franek F. Combined finite element-boundary element 708 method modelling of elastic multi-asperity contacts. Proceedings of the Institution of Mechanical 709 Engineers, Part J: Journal of Engineering Tribology. 2009;223(5):767-76. 710 45. Ilincic S, Tungkunagorn N, Vernes A, Vorlaufer G, Fotiu P, Franek F. Finite and boundary 711 element method contact mechanics on rough, artificial hip joints. Proceedings of the Institution of 712 Mechanical Engineers, Part J: Journal of Engineering Tribology. 2011;225(11):1081-91. 713 46. Andersson J. Modelling of wear and tribofilm growth. 2012. 714 47. J. Andersson AA, R. Larsson. Numerical simulation of a wear experiment. Wear. 715 2011;271(11):2947-52. 716 48. Bosman R, Schipper DJ. Mild Wear Prediction of Boundary-Lubricated Contacts. Tribology 717 Letters. 2011;42(2):169-78. 718 49. Joel Andersson, Roland Larsson, Andreas Almqvist, Grahnb M, Minami I. Semi-deterministic 719 chemo-mechanical model of boundary lubrication. faraday Discussions. 2012;156(1):343-60. 720 50. Morales-Espejel G, Brizmer V, Piras E. Roughness evolution in mixed lubrication condition due 721 to mild wear. Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering 722 Tribology. 2015:1350650115577404. 723 51. Morales-Espejel GE, Brizmer V. Micropitting modelling in rollingsliding contacts: Application 724 to rolling bearings. tribology transactions. 2011;54(4):625-43. 725 52. Ghanbarzadeh A, Wilson M, Morina A, Dowson D, Neville A. Development of a New Mechano- 726 Chemical Model in Boundary Lubrication. Tribology International. 2016;93:573-82.

727 53. Ghanbarzadeh A, Parsaeian P, Morina A, Wilson MC, van Eijk MC, Nedelcu I, et al. A Semi- 728 deterministic Wear Model Considering the Effect of Zinc Dialkyl Dithiophosphate Tribofilm. Tribology 729 Letters. 2016;61(1):1-15. 730 54. Tonder YZHaK. Simulation of 3-D random rough surface by 2-D digital filter and Fourier 731 analysis. International journal of machine tools and manufacture. 1992;32(1):83-90. 732 55. Xuefeng Tian BB. A Numerical Three-Dimensional Model for the Contact of Rough Surfaces by 733 Variational Principle. 1996. 734 56. F Sahlin RL, A Almqvist, P M Lugt and P Marklund. A mixed lubrication model incorporating 735 measured surface topography. Part 1: theory of flow factors. Proceedings of the Institution of 736 Mechanical Engineers, Part J: Journal of Engineering Tribology. 2009;224(4):335-51. 737 57. Blok H. The flash temperature concept. Wear. 1963;6(6):483-94. 738 58. Kennedy F. Frictional heating and contact temperatures. Modern tribology handbook. 739 2001;1:235-59. 740 59. Tian X, Kennedy FE. Maximum and average flash temperatures in sliding contacts. Journal of 741 Tribology. 1994;116(1):167-74. 742 60. Gosvami N, Bares J, Mangolini F, Konicek A, Yablon D, Carpick R. Mechanisms of antiwear 743 tribofilm growth revealed in situ by single-asperity sliding contacts. Science. 2015;348(6230):102-6. 744 61. Naveira-Suarez A, Tomala A, Pasaribu R, Larsson R, Gebeshuber IC. Evolution of ZDDP-derived 745 reaction layer morphology with rubbing time. Scanning. 2010;32(5):294-303. 746 62. Ghanbarzadeh A. Mechano-Chemical Modelling of Boundary Lubrication. UK: University of 747 Leeds; 2016. 748 63. Aktary M, McDermott MT, McAlpine GA. Morphology and nanomechanical properties of ZDDP 749 antiwear films as a function of tribological contact time. Tribology letters. 2002;12(3):155-62. 750 64. Gabi Nehme RM, Pranesh B. Aswath,. Effect of contact load and lubricant volume on the 751 properties of tribofilms formed under boundary lubrication in a fully formulated oil under extreme 752 load conditions. Wear. 2010;268(9):1129-47. 753 65. Ramoun Mourhatch PA. Tribological behavior and nature of tribofilms generated from 754 fluorinated ZDDP in comparison to ZDDP under extreme pressure conditionsPart II: Morphology and 755 nanoscale properties of tribofilms. tribology international. 2011;44(3):201-10. 756 66. M.A. Nicholls PRN, G.M. Bancroft, M. Kasrai, T. Dob, B.H. Frazerc and G. De Stasio. Nanometer 757 scale chemomechanical characterization of antiwear films. Tribology Letters. 2004;17(2):205-16. 758 67. Crobu M, Rossi A, Mangolini F, Spencer ND. Tribochemistry of bulk zinc metaphosphate 759 glasses. Tribology letters. 2010;39(2):121-34. 760 68. Spikes H. The history and mechanisms of ZDDP. Tribology Letters. 2004;17(3):469-89. 761 69. Yin Z, Kasrai M, Fuller M, Bancroft GM, Fyfe K, Tan KH. Application of soft X-ray absorption 762 spectroscopy in chemical characterization of antiwear films generated by ZDDP Part I: the effects of 763 physical parameters. Wear. 1997;202(2):172-91. 764 70. Martin JM, Grossiord C, Le Mogne T, Bec S, Tonck A. The two-layer structure of Zndtp 765 tribofilms: Part I: AES, XPS and XANES analyses. Tribology international. 2001;34(8):523-30. 766 71. S. Bec AT, J. M. Georges, R. C. Coy, J. C. Bell and G. W. Roper. Relationship between mechanical 767 properties and structures of zinc dithiophosphate anti-wear films. Proceedings of the Royal Society A: 768 Mathematical, Physical and Engineering Science. 1999;445(1992):4181-203. 769 72. Demmou K, Bec S, Loubet J-L, Martin J-M. Temperature effects on mechanical properties of 770 zinc dithiophosphate tribofilms. Tribology international. 2006;39(12):1558-63. 771 73. Rossi A, Piras F, Kim D, Gellman A, Spencer N. Surface reactivity of tributyl thiophosphate: 772 effects of temperature and mechanical stress. Tribology Letters. 2006;23(3):197-208. 773 74. De Donato P, Mustin C, Benoit R, Erre R. Spatial distribution of iron and sulphur species on the 774 surface of pyrite. Applied Surface Science. 1993;68(1):81-93. 775 75. Zerulla D, Mayer D, Hallmeier K, Chassé T. Angular-resolved XANES measurements of the polar 776 and azimuthal orientation of alkanethiols on InP (110). Chemical physics letters. 1999;311(1):8-12.

777 76. Heuberger RC. Combinatorial study of the tribochemistry of anti-wear lubricant additives: 778 Diss., Eidgenössische Technische Hochschule ETH Zürich, Nr. 17207, 2007; 2007. 779 77. Brow RK, Tallant DR, Myers ST, Phifer CC. The short-range structure of zinc polyphosphate 780 glass. Journal of Non-Crystalline Solids. 1995;191(1):45-55. 781 78. Nicholls MA, Do T, Norton PR, Kasrai M, Bancroft GM. Review of the lubrication of metallic 782 surfaces by zinc dialkyl-dithiophosphates. Tribology international. 2005;38(1):15-39. 783 79. Wang W, Wong P, Zhang Z. Experimental study of the real time change in surface roughness 784 during running-in for PEHL contacts. Wear. 2000;244(1):140-6. 785 80. Jamari J. Running-in of rolling contacts: University of Twente; 2006.

786

787